O'Connell and Weeks [5] adopt the second representation and introduced a set-recoding scheme that further reduces the length of the single-locus genotype lists and accelerate the summations over multilocus genotypes to create a program that is both fast and memory efficient: VITESSE ( vitesse is the French for speed). We briefly explain their recoding scheme below.
First, the alleles present in the pedigree are split into
``transmitted'' and ``non-transmitted'' sets of alleles. For each
individual, the transmitted alleles are defined as alleles for which
there exist a transmission path through unobserved individuals to an
observed descendant. Remark: that does not mean that these alleles
were actually transmitted but rather that they could have been. The
other alleles that could be present in the individual but are not
observed in his descendants are termed non-transmitted. The example in
figure 1 illustrate the concept. Only 4, 7, 9 and 10
are genotyped for a 4-allele marker. The set of transmitted alleles
for individual 1 is 
since these 3 alleles are
found in her descendants and her set of untransmitted alleles is 
. The genotype of individuals 7 and 8 can be inferred from the
genotypes of their offspring to be 2,3. For these two individuals,
and 
. Individual 11 has 
and 
since he has no descendents.
Inheritance relations must be redefined for these allele sets. An individual has genotype A|B where A and B, instead of being the alleles inherited from his mother and from his father, are subsets of the individual's set of transmitted alleles, A being the set of alleles possibly inherited from the mother and B the set from the father.
An offspring of that individual inherits a set of alleles C formed by
set inclusion (
or 
) instead of allele
equality (A=B or B=C). The authors call it ``fuzzy inheritance''
by analogy to fuzzy logic. A proof that using transmission probabilities
generated by fuzzy inheritance does not alter the likelihood is
presented in O'Connell and Weeks [5].
The authors present the results of tests showing that VITESSE outperforms FASTLINK for multilocus computations with polymorphic markers both in time and memory requirement. VITESSE can handle larger pedigrees and more loci. However, because VITESSE sums over multilocus genotypes, even a restricted number of them, the programs hits its limits with 6 or 7 markers. It is noteworthy that all the examples illustrating success with VITESSE involve only a single founder couple, and have no loops. The class of pedigrees on which VITESSE will succeed is not yet clear.
